An isoperimetric inequality for Gauss-like product measures
نویسندگان
چکیده
منابع مشابه
On the Isoperimetric Constants for Product Measures
This quantity was introduced in 1969 by Cheeger [1] to bound from below the spectral gap of the Laplacian on compact Riemannian manifolds, and nowadays (1) is often called an isoperimetric inequality of the Cheeger type. The relationship between more general isoperimetric and certain Sobolev type inequalities was earlier considered by Maz’ya [2] (see for history, for example, [3, 4]). What was ...
متن کاملIsoperimetric Constants for Product Probability Measures
Received July 1995; revised April 1996. 1Research supported in part by ISF Grant NXZ000 and NXZ300 and by the Alexander von Humboldt-Stiftung. This author enjoyed the hospitality of the Faculty of Wiskunde and Informatica, Free University of Amsterdam and of the Faculty of Mathematics, Bielefeld University, while part of this research was carried out. 2Research supported in part by an NSF Postd...
متن کاملAn Asymptotic Isoperimetric Inequality
For a finite metric space V with a metric ρ, let V n be the metric space in which the distance between (a1, . . . , an) and (b1, . . . , bn) is the sum ∑n i=1 ρ(ai, bi). We obtain an asymptotic formula for the logarithm of the maximum possible number of points in V n of distance at least d from a set of half the points of V , when n tends to infinity and d satisfies d √ n. 1 The Main Results Le...
متن کاملAn Isoperimetric Inequality for the Heisenberg Groups
We show that the Heisenberg groups H 2n+1 of dimension ve and higher, considered as Rieman-nian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area L 2). This implies several important results about isoperimetric inequalities for discrete groups that act either on H 2n+1 or on complex hyperbolic space, and provides interesting ex...
متن کاملAn isoperimetric inequality for the Wiener sausage
Let (ξ(s))s≥0 be a standard Brownian motion in d ≥ 1 dimensions and let (Ds)s≥0 be a collection of open sets in R. For each s, let Bs be a ball centered at 0 with vol(Bs) = vol(Ds). We show that E[vol(∪s≤t(ξ(s) + Ds))] ≥ E[vol(∪s≤t(ξ(s) + Bs))], for all t. In particular, this implies that the expected volume of the Wiener sausage increases when a drift is added to the Brownian motion.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2016
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2016.02.014